Spanning Class in the Category of Branes
Andr\'es Vi\~na

TL;DR
This paper constructs a specific line bundle on a generic anticanonical hypersurface in a toric variety, establishing it as a spanning class in the derived category and exploring related string spaces and gauge fields.
Contribution
It introduces a line bundle that generates a spanning class in the derived category of the hypersurface and analyzes associated string spaces and gauge fields.
Findings
Proves the line bundle generates a spanning class in D^b(Y)
Establishes a vanishing theorem for vertex operators
Defines a Yang-Mills minimizing gauge field on the line bundle
Abstract
Given a generic anticanonical hypersurface of a toric variety determined by a reflexive polytope, we define a line bundle on that generates a spanning class in the bounded derivative category . From this fact, we deduce properties of some spaces of strings related with the brane . We prove a vanishing theorem for the vertex operators associated to strings stretching from branes of the form to nonzero objects in . We also define a gauge field on which minimizes the corresponding Yang-Mills functional.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Nonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology
